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.. (לתיקייה המכילה) | |
HW5 q1 - How exactly to estimate the attainable accuracy? | |
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The purpose is to practice some basic estimations that you can do in your head. (It may help in situations where all you got is your head...). You can see that the obtainable accuracy's formula uses: q = the multiplicity (Ribuy) of the root, and the lower bound of the q-th derivative (in absolute value) at the root's area. To find a section with the root, you can say "g(x) is defined only when x>0. so g(x)=x+ln(x)=0 in a place where ln(x) is negative". -- continued |
HW5 q1 cont. | |
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To estimate the bound of the derivative, it may be easier if you say: f'(x) = something1 + something2 , so the lower bound of f'(x) is the sum of the lower bounds of the two parts. I prefer to see here good common sense and simplicity, rather than rigorous calculation. I'm not trying to make you a hard life... About the "ribuy" (which we call q), if you show that f'(root) != 0, then q=1. If f'(root)=0 and f''(root)!=0 then q=2. and so on. You DON'T have to know the root in order to show it! |